Space Warship Design III: Final Considerations

In this post, we'll look at some final considerations required to complete out baseline warship.

Point Defense

Sky full of anti-aircraft flak during naval battle of Santa Cruz

In space, nothing stops a projectile from travelling to extreme distances, and the effectiveness of a beam weapon tapers off gradually. 'Point' defense doesn't exist in space, but we will continue to use it to mean the last line of defense a warship has against incoming projectiles.

Lasers, kinetics and anti-missile missiles are the three types of defense possible. A wide-angle Casaba Howitzer can sweep away one wave of missiles, but as it is essentially a nuclear explosion, it could potentially mission-kill the warship it is defending (radiation flux, flash burn of exposed sensors, heat warping of main laser mirror ect.)....

Laser Point Defense

A regular missile launched at a 1000km stand-off distance will spend 90% of its life under fire from the target's main laser. This weapon has the longest range, and it must start firing immediately after detecting a launch to maximize the number of missiles shot down. As the range closes, the beam can be focused to ever smaller spots, leading to more watts per square meter and faster penetration of the missile's armor. If we analyze the effectiveness of a laser simplistically, we would have to set the maximum penetration rate at infinity as distance closes to zero. 

This is not the case in practice. A laser will take a certain amount of time to switch the beam from burning through one target to another. At very long ranges, missiles will appear close to each other, with angular separations on the order of a hundredth of a degree. Adjusting the beam can be done through the main mirror's natural adaptive optics. Even if the missiles accelerate into oblique trajectories, the time it takes to adjust the main mirror by several degrees is negligible compared to the time it takes for the beam to burn through one missile's armor. 

However, at short ranges, the main mirror cannot keep this up. Switching between targets takes longer and longer as angular separation increases. Moving the main mirror starts taking longer than the time to burn through a missile. It becomes more sensible to divide the main beam through several channels and focus it through small mirrors mounted in rapidly swiveling turrets. Or is it? Let's find out.

Point defense lasers from the 2009 Star Trek movie's opening scene

The small diameter of these 'point defense' turrets' mirrors would normally reduce their effective range greatly, but it is more than sufficient for the last 100km of a missile's trajectory. 

A possible configuration would be six (one for each axis, in fore and aft positions) 60cm wide mirror using the 400nm beam of the main laser weapon, dividing the 250MW beam between them. As kinetic attacks are seldom launched from both the front and rear, four such turrets will be brought into play against the targets. They would produce 62.5MW each. Laser fire can be added to target the same missile for a full 250MW blast, or divided between four individual targets.

Penetration rates:

100km: 17.6mm/s, x4: 70.4mm/s

50km: 141mm/s

10km: 17.6m/s

1km:   17.6km/s

As you can see, penetration rates are extreme as the range closes. However, penetration rates of a few kilometers per second are only due to the pinpoint spot size the beams are concentrated to, and are neither useful nor practicable. Burning narrow holes through a missile will not force it to change its course nor reduce its penetrative power. At the end of its trajectory, the missile will have very few to no propellants remaining on-board, so it is basically inert and already set on a collision course.

Holes created by a pulsed laser

Such holes would also have an extreme 'aspect ratio': the width of a hole compared to its depth. Hemispherical craters have an aspect ratio of 1. Kinetic impacts produce aspect ratios of about 20, and lasers with stabilized beams and immobile targets will reach an aspect ratio of 50 before they start scraping the walls. Tunneling through kilometers per second would need a hole of similar width. 

Lasers traditionally aim for the smallest spot size possible. If our point defense turrets try to do the same, they will not do significant damage to the missiles. Instead, point defense lasers should increase the spot size to cover the entire missile and maximize the mass of carbon vaporized per second. If enough of the missile's armor is vaporized, it will blow it off-course at long ranges, or try to reduce it to slag at short ranges.

Laser ablation of an asteroid.

At 100km distance, the edge of the point defense zone, missiles only need to be deflected by a slight amount (a handful of meters per second) for them to miss their target. At 1km distance, they'd need to deflect by hundreds of meters per second, laterally. This is extremely inefficient in terms of energy and time expended per missile: the missile can point its nose at the laser and prevent the ejected material for pushing it in the wrong direction.

The other option is complete destruction of the missile.

The 5kg missile mentioned in Part II of this series will mass 4.4kg after its propellant has been expended. 4.4kg of diamond-like carbon requires 37 MJ to be absorbed for it to be melted, and about 131MJ to be vaporized. The actual figure will lie closer to 131MJ, as the carbon armor is optimized for absorbing a maximum amount of laser energy before ablating, instead of conducting that energy to the rest of the missile and allow for relatively slower fusion. 

A 62.5MW beam would have to focus on the target for two seconds at most. With four such beams, the target warship can destroy 20 missiles. If it takes a second to switch between missiles, the performance is reduced to 13 missiles. This number is not good. It is less than what two coil-gun launched missiles busses can deliver, and combat will involve dozens of those. 

Another solution is to 'think outside of the box' and stop designing point defenses the same way the main laser weapon is designed. Instead of focusing on spot size and compensating with rapid rotation rate, we must optimize for the situation at hand.

The number of missiles destroyed can be drastically increased by using laser 'broadsides' instead of bulky turrets. These are small mirrors they are sunk into pits along the flanks of the warship. The mirrors can mechanically shift their focal point along a cone of vision and can be shuttered when not in use. They can be as small as 30 cm in diameter, and able to focus 100% of their energy on a missile at 100km (spot size 16cm) using the main laser's 400nm beam, or at 40km using the Gyrotron's 1000nm beam. A microwave beam will provide equal power on target to the optical beam up to 52km, assuming 60% VECSEL efficiency, and will output more total energy within 100km than the 400nm beam.

Broadside lasers on a warship from Gunbuster

We will mount more lasers than the generators can power, to compensate for battle damage. Based on current 30cm telescopes mounted on electric tripods, a 100kg assembly, minus cooling, is possible. Assuming the microwave beam is being used, about 25 missiles will be destroyed, which is double what is possible with the turrets. The main advantage is that switching time is reduced to insignificance, and the heat load is distributed between multiple laser optics. 

Kinetic PD

Even with an impressive number of megawatts, laser point defenses take time to destroy a missile. They suffer from over-heating issues, and are power limited: you cannot ramp up power output in response to emergencies. Yes, given time to cool down, they can be used again and again, indefinitely, and force a minimum 'threshold' number of missiles required to take down a warship. However, they will be defeated by 'peak' loads, and all missile combat against lasers relies on this fact.

Sea Wolf missile launching from VLS.

Kinetic Point Defense is the other shoes. It shines in 'peak' situations where lasers fail, but relies on lasers for a complete defense.

The main advantage of kinetic PD over lasers is that you can launch all your defensive projectiles at once. There is no limit to the numbers you can launch, and the rate of fire is practically unlimited. 

However, there are limits. Relying on Kinetic Point-Defense means that while you can fend off endless waves of missile attacks (defensive missiles can be much smaller and lighter than attack missiles, so the defending target will always carry more of them), the ammunition required will cut heavily into your offensive budget. Continuously defending is not a victory condition. Kinetics do have to stop firing periodically to reload. Their range is extremely limited, meaning it is hard to defend an adjacent spaceship and group the defensive fire the way it is possible to do with lasers. 

Metal Storm's method of stacking bullets to achieve incredible rates of fire.

Despite these limits, Kinetic PD is extremely effective. It will not take the form of rapid-fire guns that we are familiar with today. Instead, it is a combination of plate drones are reactive EFP. Plate drones are robotic craft with limited on-board deltaV, launched into the path of an incoming missile. They only need to match the lateral movements of a missile. When a missile strikes a plate, it is broken up by the impact into smaller pieces that cannot penetrate the main armor. Reactive Explosively-Formed-Projectile bricks are pieces of 'active' armor that work on very short distances. When they detect a projectile that they are able to intercept, usually at distances of 1-2km, they detonate and fling a metal projectiles at velocities of about 2.5km/s outwards. The impact results in the complete destruction of the missile.

THAAD-25 kinetic kill missile. 

Plate Drones are launched by a low-velocity coilgun, from multiple ports, at rates of over 100 drones per second. They mass about 3 kg: 2kg is a high density plastic plate of 1m diameter and 2mm thickness, 300g is electronics and actuators,  and 700g is Electric Solid Propellant charges. Total deltaV is about 530m/s. A missile cutting clean through a plate will absorb 3MJ of energy, the equivalent of 700g of TNT. This is enough to obliterate the missile in optimal conditions. Plate Drones can be defeated by a preceding wave of sand munitions, or by accurate laser attack.

A reactive EFP striking the missile will have even more devastating results, with energies around 35-45MJ being released. 

Putting the numbers together, we get a clear picture:
-You can respond to a 1000 ton wave of missiles with only 60 tons of defensive Plate Drones in a worst case scenario (no sand, no lasers). 
-Laser defenses increase the threshold for 'successful' missiles getting through the main laser defenses by another 250 tons of ordinance... per standard laser available.
-You can add a layer of reactive armor at about 400kg/m^2 to defeat missiles that slip through all previous defenses.

We can conclude that direct attack by missiles is a risky move that puts the attacker at a strict mass disadvantage. Unless there is a situation that drastically favors a kinetic attack, such as high closing velocity, it should not be attempted. Even in perfect conditions, such as seeding the missile wave with bursts of sand munitions to clear away Plate Drones or knock out reactive EFP sensors, or having a cold laser on-hand to sweep away those defenses, offensive missiles have to accelerate themselves to crossing velocities, while defensive projectiles do not.

The only solution for an equitable exchange is stealth projectiles.

We will set 100kg as the mass requirement for a 'broadside' defensive laser. A Plate Drone masses 3kg, and is launched by a 1 ton 1.5MW railgun. Reactive armor masses 400kg per square meter. 

Mass Ratio and Mission dV

All the previous figures set so far allow us to work out a 'dry mass' for our baseline warship. Now, we must establish the mission that the warship is expected to perform, and from that, the deltaV is must be able to produce.

Putting the deltaV requirement and the engine's exhaust velocity together, we obtain the 'wet mass': the mass of the spaceship fully loaded with propellant.

Let's start with the Terran spaceships. As mentioned in Part I of this series, the Terran fleet is designed to project Earth's power to its colonies around the Solar System. In this case, they must be able to quickly present themselves in the Martian system, while remaining stationed around Earth. We have already worked out that Terran warships use a separate interplanetary stage with different propellant and drive characteristics from the combat stage.

The different stages of a mission (departure, combat, return ect.) require set amounts of deltaV. Putting the requirements together creates a 'deltaV budget', where instead of money, you have propellant in the tanks. Thinking of deltaV as a budget is useful, as it allows us to understand that performing an acceleration burn now will leave you will less deltaV for later, and that small savings made throughout the mission can give you a safety margin in critical moments.

DeltaV, distance and time are all interlinked. Longer distances require more deltaV for a set amount of time, while it takes longer to cross the same distance with less deltaV. Based on the objective set out in Part I of this series, we want the Terran spaceships to reach Mars in about 1 month.

Mars closest distances at various dates. In miles...

The straight-line distance between Earth and Mars varies between 56 and 401 million kilometers. Working with averages, crossing 225 million kilometers in 1 month requires an average velocity of 86km/s. At this velocity, it would take a one week trip to reach Mars at its closest approach, and 7 weeks at most. 

At these velocities, we can ignore orbital movement and work with straight lines. Accelerating to 86km/s requires an equal deceleration at the destination, so a total 172km/s of deltaV is required for the outbound trip. The return trip will likely be much less urgent. Either the Terran fleet is victorious and refuels, or it loses. If it loses, it is utterly destroyed. In the rare cases where the defending fleet is too damaged to pursue, the Terran fleet will take the long way back home. Such a trip can be accomplished with a minimal Hohmann trajectory, requiring a minimum of 3km/s to a maximum of 10km/s. The total deltaV required from the interplanetary booster is 182km/s.

A Pulsed Inductive Thruster producing up to 9000Isp at 80MW/ton, or 88.3km/s exhaust velocity, was set as the propulsion for the Terran warship's interplanetary booster. 

To work out the mass ratio of a spaceship with such an engine, tasked with producing a deltaV budget, we use this equation:

• Mass ratio: e^( DeltaV / Exhaust Velocity )

In this case, DeltaV is 182km/s, and exhaust velocity is 88.3km/s. We work out a mass ratio of 6.18

This means that the interplanetary stage, departing from Earth will be 84% propellant. 

The combat stage needs only to spend propellant combat. Since it does not really have to go anywhere, the deltaV requirement is more a function of how many seconds of acceleration it must be capable of. The second requirement is to have a good mass ratio: too high a deltaV budget will translate into huge amounts of propellant. A warship cannot afford to have enormous, vulnerable propellant tanks. They become a weakpoint that is excessively disadvantageous to try to cover with armor, and cuts into the warship's ability to quickly dodge an incoming wave of kinetics.

A 1000 ton (dry mass) warship might dedicate 100 tons of its mass to propulsion. This will give it 100GW of propulsive power. If it uses open-cycle gas-core nuclear engines, it will produce a jet with 20km/s exhaust velocity and 8 Meganewtons of thrust.

A warship carrying 1000 tons of water propellant will be able to accelerate at a rate between 4 and 8m/s^2. If a wave of missiles is detected early, then it leisurely force the missiles to expend their 500m/s maneuvering deltaV by accelerating at a regular 5m/s^2, and it can do this for 46 minutes. If stealth missiles approach detection range, the warship can 'dump the core' by flooding the reaction chamber with water and drastically lowering exhaust velocity to gain thrust. This would snuff out the nuclear flame, and the reactor would take time to be cleared of water, injected with uranium gas and heated to critical density again.

Acceleration requirements between laser craft are situational. If the laser warships are mismatched in range and power, one side will try to escape by out-accelerating the other for as long as possible. If both believe that the difference in their maximal acceleration is too small, they will conserve propellant to be used as a heat sink, thereby lengthening the time their lasers can fire while cool and accurate.

Terran warships will usually be entering a planetary system after performing a lengthy insertion burn. They will then detach from the interplanetary stage and leave in a very high orbit. These warships must then rely on their own propellant reserves to lower themselves to a lower orbit and engage the defending forces. The transition between high and low orbit can cost upwards of 6km/s around Mars. 

F-16 with drop tanks.

Instead of halving their combat reserves, Terran warships will carry drop tanks. Due to their more advanced propulsion technology, we can add that Terran warship can nuclear drives that can function with Liquid Hydrogen. This would more than double their exhaust velocity at a time where thrust is unimportant. The Liquid Hydrogen would be drawn from the Interplanetary stage's reserves, and could serve to cool down spaceships that rely on stealth. 

For a 1000 ton warship carrying 1000 tons of water, and 40km/s exhaust velocity on Liquid Hydrogen, 6km/s of deltaV would require 283 tons of propellant.

Martian warships face a very different situation.

They are a defensive fleet, meaning that they do not ever intend to cross interplanetary distances. The Martian warships therefore do not use an interplanetary stage. Furthermore, they are defending their home territory. This means that they are supported by the full might of their orbital infrastructure: they can afford to retreat and refuel. 

Martian warships using nuclear gas-core engines will be used to engage Terran warships with similar engines and performance, so they will resemble their targets. To keep Terrans within their lower weapons ranges, they need higher accelerations, so more of their dry mass is dedicated to engines. The deltaV requirements however, can be lower (500 tons of water gives 8.2km/s deltaV), as they can afford to rely on a fleet of tankers to refuel them. 

Martians will use more primitive solid-core nuclear thermal rockets to intercept invaders. These have much lower exhaust velocity than gas core engines, but excel at delivering high specific power (2GW/ton or more) without requiring huge radiators. With liquid hydrogen, exhaust velocity is 8km/s, but with water, it falls to 4km/s. A maximum velocity intercept will require 16km/s: 10km/s outbound, 5km/s to fall under Mars escape velocity, and a small 1km/s to adjust their slow return to be captured by allies. This would require a mass ratio of 6 with liquid hydrogen, but the initial 10km/s can be carried in drop tanks.

A 1000 tons (dry mass) interceptor would need to carry 5000 tons in drop tanks, and 900 tons in internal tanks. They would have to rely on stealth to compensate for the lack of combat deltaV, which is facilitated by the huge amounts of cryogenic liquid it carries.    

Baseline Spaceship

So, we now have all of the figures ready to put together into a baseline spaceship. Mind you, while this is a good reference to use when designing spaceships that actually fly in the setting, they are as useful as the design for a generic car: it would never provide a practicable design that might be built.

A baseline spaceship's main function is during worldbuilding, when you need to be able to tell whether your 'fast' warship is actually faster than the reference, or when your 'heavy cruiser' actually masses more than the norm. It also allows you to skip certain steps, such as working out crew requirements or electronics mass.

We'll start with 5GW.

Propulsion masses 50 tons. With an open-cycle gas core nuclear engine, it can produce 50GW of propulsive power. At 80% efficiency, this is 4 MN of thrust at 20km/s exhaust velocity. Running total: 50 tons.

The reactor produces 10GW of waste heat. 5GW is absorbed by the reactor walls. This heat is absorbed by a lithium coolant heat exchanger, and passed onto an ionized plasma and run through an MHD generator. At 30% efficiency and 10MW/ton, it masses 166 tons, generates 1.66GW and releases 3.34GW of waste heat. Running total: 216 tons.

3.34GW of waste heat can removed by 90% emissivity radiators operating at 1200K. It would require four double-sided fins of 3883m^2, massing a total of 528 tons. Running total: 744 tons.

Using water, tank mass is 1% of propellant mass or less. This is 20 tons for 2000 tons of water, with a deltaV of 13.8km/s and 2.5 hours of burn at maximum acceleration (between 1 and 2m/s^2). Running total: 764 tons.

A crew of 3 individuals is required. They expect to stay up to 3 months in a warship. They need 0.79 tons of consumables. Based on inflatable modules, living space modules will cost 3 tons but provide about 50m^3. Running total: 767.8 tons.

This warships is equipped with three wide-angle sensors and a single narrow-angle sensor. Actual designs will have different numbers based on their role in a fleet, but for now we'll dedicate 5 tons to sensors. Running total: 772.8 tons.

1.66GW of electrical energy will be divided between electrical systems, life support, heat pumps and a Gyrotron/VECSEL laser weapon. Electrical and life support consumption should be under a handful of megawatts, so can be ignored. Nonetheless, a 1 ton backup nuclear reactor at 5% efficiency can required in case the main reactor or power generators are offline. Running total: 773.8 tons.

A laser weapon has three main components: mirror, generator, heat pumps. Heat pumps are vital in reducing radiator mass. 

The spaceship will use a 4m radius mirror. It will mass 2 tons, based on a 40kg/m^2 figure for adaptive optics. Two replacement mirrors add 4 tons. Running total: 779.8 tons.

1.66GW has to be shared between heat pumps, that move 1.25W of waste heat per 1W consumed, and the laser generator, that produces 0.52W of waste heat per 1W consumed. A 1.15GW laser generator produces 598MW of waste heat, which is increased from 500K to 1500K temperature by heat pumps consuming 478MW of energy.

1.15GW goes to a Gyrotron that masses 115 tons. It produces a 920MW microwave beam. A 12 ton VECSEL array converts this beam to 552MW of near-ultraviolet light. The total mass is 127 tons. Running total: 906.8 tons.

The heat pumps have a specific power of only 2MW/ton, and therefore mass 239 tons. The laser radiator has a surface area of 2278m^2, which can be divided into four double-sided fins of 284m^2. They would mass a total of 38.7 tons. Running total: 945.5 tons.

Laser point defenses will be able to use the full 920MW laser beam generated by the Gyrotron. With a 7 second range against 10km/s projectiles, it is expected to shoot down 50 missiles. This can be handled by 12 'broadside' lasers per flank, for a total of 36 tons. Running total: 981.5 tons.  

Electronics add another 1% (instead of modern 3-8% figures) to this dry mass. Running total: 991.3 tons. 

Internal structural components another 10% to that. Running total: 1090.4 tons. 

Against a kinetics warship with 1000 tons of ammunition, this warship can expect a maximum of 100 tons of kinetic impacts coming its way. These can be dealt with by using 20 tons of plate drones. Running total: 1110.4 tons.

A warship should average about 1000kg/m^3 density in its construction. This means that 1110 tons would fit in 1110m^3. The overall shape, however, is a narrow cone of 15 degrees angle (the mirror shoots out of a dielectric mirror transparent to the specific wavelength being used). This means the internal dimensions are 39m length and 5m radius. The propellant tank is a cylinder 10m wide and 25m long. 

The cone has a surface area of 712m^2. It requires laser armor and kinetic armor. Laser armor for a single-shell rotating cylinder, made to withstand 20 minutes of laser fire against 3 250MW opponents, is 460kg/m^2 of diamond-like carbon. It masses 327.5 tons.  Running total: 1437.9 tons. 

Kinetic armor will form three armor belts. Belt A is a 1m thick armor belt at the base of the cone, of 3m length, protects the crew, life support, backup generator and vital electronics. Belt B is a 0.4m thick armor belt, halfway up the cone, of 5m length protects the laser generator and heat pumps. Belt C is a 0.4m thick armor belt protects the nuclear engine and main power generator at the rear, of 5m length.

Belt A has an inner radius between 5.13m and 4.74m, averaging 4.94m. Outer radius is 5.94m. It has a volume of 102.5m^3 and masses 235 tons. Running total: 1672.9 tons.

Belt B has an inner radius between 3.29m and 2.63m, averaging 2.96m. Outer radius is 3.36m. It has a volume of 39.7m^3 and masses 91.3 tons. Running total: 1763.8 tons.

Belt C has an inner radius of 5m, and an outer radius of 5.4m. It has a volume of 65.3m^3 and masses 150.2 tons. Running total: 1914 tons.

We can now freely distribute 86 tons between reactive armor bricks and small systems, such as radio dishes, airlocks, maneuvering jet thrusters and so on. Running total: 2000 tons.

The Baseline Spaceship masses 2000 tons dry, 4000 tons wet. It can accelerate between 1 and 2 m/s^2 for two hours and a half. It can engage targets at 6500km (1.7mm/s carbon penetration rate) and defend itself from the full ammunition load of a direct-fire kinetics ship. It can withstand 27 minutes of laser fire from three standard 250MW lasers before sustaining damage. Its kinetic armor belts can fend off 5kg impactors, with vital areas withstanding 20kg impacts. The crew has provisions for 3 months, but can survive for much longer if it accepts to drink slightly irradiated propellant water.

In actual combat, it is a terrible ship. If it wanted to become effective at laser ranges, it will invest into larger mirrors and droplet radiators. It can defend itself against kinetic missiles that make no attempt at stealth, but actual missiles waves are a mix of direct fire, nuclear, sand and stealth warheads. Its acceleration is lower than what a solid-core nuclear thermal rocket is capable of, yet it does not invest in deltaV or liquid hydrogen propellant to beat it out in the long run. 

In the next and final post of this series, we will design two actual warships.